If two add-ons use the same application handler, is there a way to see (or force) which add-on executes first?
The callable is been called in sequence where in bpy.app.handlers.frame_change_pre
As a easy snippet here:
import bpy
#pre and post running seq are same direction
fcp = bpy.app.handlers.frame_change_pre 
fcp.clear() #clear the list for testing only

def myfunction(*args):
    print(&quot;My first func&quot;)

fcp.append(myfunction)
fcp.append(lambda *args:print(&quot;Second lambda&quot;))

print(fcp)

After excute, change 1 frame and the console output:
[&lt;function myfunction at 0x000002A5E4C37A68&gt;, &lt;function &lt;lambda&gt; at 0x000002A5E4BF4F78&gt;]
My first func
Second lambda

So you can some how insert your code at the begin of list:

bpy.app.handlers.frame_change_pre.insert(0, your_function)

Or determine where your function is in the right position:
my_index = fcp.index(myfunction)
fcp.pop(index = my_index)
fcp.insert(0, myfunction)